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The global-in-time energy estimate is derived for the second-order accurate exponential time differencing Runge-Kutta (ETDRK2) numerical scheme to the phase field crystal (PFC) equation, a sixth-order parabolic equation modeling crystal evolution. To recover the value of stabilization constant, some local-in-time convergence analysis has been reported, and the energy stability becomes available over a fixed final time. In this work, we develop a global-in-time energy estimate for the ETDRK2 numerical scheme to the PFC equation by showing the energy dissipation property for any final time. An a priori assumption at the previous time step, combined with a single-step $H^2$ estimate of the numerical solution, is the key point in the analysis. Such an $H^2$ estimate recovers the maximum norm bound of the numerical solution at the next time step, and then the value of the stabilization parameter can be theoretically justified. This justification ensures the energy dissipation at the next time step, so that the mathematical induction can be effectively applied, by then the global-in-time energy estimate is accomplished. This paper represents the first effort to theoretically establish a global-in-time energy stability analysis for a second-order stabilized numerical scheme in terms of the original free energy functional. The presented methodology is expected to be available for many other Runge-Kutta numerical schemes to the gradient flow equations.

Urban traffic resilience has gained increased attention, with most studies adopting an engineering perspective that assumes a single optimal equilibrium and prioritizes local recovery. On the other hand, systems may possess multiple metastable states, and ecological resilience is the ability to switch between these states according to perturbations. Control strategies from these two resilience perspectives yield distinct outcomes. In fact, ecological resilience oriented control has rarely been viewed in urban traffic, despite the fact that traffic system is a complex system in highly uncertain environment with possible multiple metastable states. This absence highlights the necessity for urban traffic ecological resilience definition. To bridge this gap, we defines urban traffic ecological resilience as the ability to absorb uncertain perturbations by shifting to alternative states. The goal is to generate a system with greater adaptability, without necessarily returning to the original equilibrium. Our control framework comprises three aspects: portraying the recoverable scopes; designing alternative steady states; and controlling system to shift to alternative steady states for adapting large disturbances. Among them, the recoverable scopes are portrayed by attraction region; the alternative steady states are set close to the optimal state and outside the attraction region of the original equilibrium; the controller needs to ensure the local stability of the alternative steady states, without changing the trajectories inside the attraction region of the original equilibrium. Comparisons with classical engineering resilience oriented urban traffic resilience control schemes show that, proposed ecological resilience oriented control schemes can generate greater resilience. These results will contribute to the fundamental theory of future resilient intelligent transportation system.

We construct new higher-order implicit-explicit (IMEX) schemes using the generalized scalar auxiliary variable (GSAV) approach for the Landau-Lifshitz equation. These schemes are linear, length preserving and only require solving one elliptic equation with constant coefficients at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates in $l^{\infty}(0,T;H^1(\Omega)) \bigcap l^{2}(0,T;H^2(\Omega))$ of orders 1 to 5 in a unified framework.

Crash data is often greatly imbalanced, with the majority of crashes being non-fatal crashes, and only a small number being fatal crashes due to their rarity. Such data imbalance issue poses a challenge for crash severity modeling since it struggles to fit and interpret fatal crash outcomes with very limited samples. Usually, such data imbalance issues are addressed by data resampling methods, such as under-sampling and over-sampling techniques. However, most traditional and deep learning-based data resampling methods, such as synthetic minority oversampling technique (SMOTE) and generative Adversarial Networks (GAN) are designed dedicated to processing continuous variables. Though some resampling methods have improved to handle both continuous and discrete variables, they may have difficulties in dealing with the collapse issue associated with sparse discrete risk factors. Moreover, there is a lack of comprehensive studies that compare the performance of various resampling methods in crash severity modeling. To address the aforementioned issues, the current study proposes a crash data generation method based on the Conditional Tabular GAN. After data balancing, a crash severity model is employed to estimate the performance of classification and interpretation. A comparative study is conducted to assess classification accuracy and distribution consistency of the proposed generation method using a 4-year imbalanced crash dataset collected in Washington State, U.S. Additionally, Monte Carlo simulation is employed to estimate the performance of parameter and probability estimation in both two- and three-class imbalance scenarios. The results indicate that using synthetic data generated by CTGAN-RU for crash severity modeling outperforms using original data or synthetic data generated by other resampling methods.

Statistical inference for high dimensional parameters (HDPs) can be based on their intrinsic correlation; that is, parameters that are close spatially or temporally tend to have more similar values. This is why nonlinear mixed-effects models (NMMs) are commonly (and appropriately) used for models with HDPs. Conversely, in many practical applications of NMM, the random effects (REs) are actually correlated HDPs that should remain constant during repeated sampling for frequentist inference. In both scenarios, the inference should be conditional on REs, instead of marginal inference by integrating out REs. In this paper, we first summarize recent theory of conditional inference for NMM, and then propose a bias-corrected RE predictor and confidence interval (CI). We also extend this methodology to accommodate the case where some REs are not associated with data. Simulation studies indicate that this new approach leads to substantial improvement in the conditional coverage rate of RE CIs, including CIs for smooth functions in generalized additive models, as compared to the existing method based on marginal inference.

In this paper we construct new fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the new generalized scalar auxiliary variable approach with optimal energy approximation (EOP-GSAV) for Cahn-Hilliard equation and consistent splitting method for Navier-Stokes equation. These schemes are linear, fully decoupled, unconditionally energy stable, only require solving a sequence of elliptic equations with constant coefficients at each time step, and provide a new technique to preserve the consistency between original energy and modified energy. We derive that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. Furthermore, we carry out a rigorous error analysis for the first-order scheme and establish optimal global error estimates for the phase function, velocity and pressure in two and three-dimensional cases. Numerical examples are presented to validate the proposed schemes., Comment: arXiv admin note: text overlap with arXiv:2009.09353

Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu and Shen in \cite{cheng2020new}, which has been broadly used to solve various challenging phase field problems. To design original energy stable schemes, they have to solve a nonlinear algebraic equation to determine the introduced Lagrange multiplier, which can be computationally expensive, especially for large-scale and long-time simulations involving complex nonlinear terms. This paper presents an essential improved technique to modify this issue, which can be seen as a semi-implicit combined Lagrange multiplier approach. In general, the new constructed schemes keep all the advantages of the Lagrange multiplier method and significantly reduce the computation costs. Besides, the new proposed BDF2 scheme dissipates the original energy, as opposed to a modified energy for the classical Lagrange multiplier approach in \cite{cheng2020new}. We further construct high-order BDF$k$ schemes based on the new proposed approach. In addition, we establish a general framework for extending our constructed method to dissipative systems. Finally several examples have been presented to demonstrate the effectiveness of the proposed approach.

In this paper, we propose two efficient fully-discrete schemes for Q-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary variable (sESAV) approach in time and the finite difference method for spatial discretization. The modified discrete energy dissipation laws are unconditionally satisfied for both two constructed schemes. A particular feature is that, for two-dimensional (2D) and a kind of three-dimensional (3D) Q-tensor flows, the unconditional maximum-bound-principle (MBP) preservation of the constructed first-order scheme is successfully established, and the proposed second-order scheme preserves the discrete MBP property with a mild restriction on the time-step sizes. Furthermore, we rigorously derive the corresponding error estimates for the fully-discrete second-order schemes by using the built-in stability results. Finally, various numerical examples validating the theoretical results, such as the orientation of liquid crystal in 2D and 3D, are presented for the constructed schemes.

The field trap effect on the microcavity surface under the action of an electric field is not conducive to boiling heat transfer. This numerical study found that using conducting-insulating microcavity surfaces in an electric field removes the field trap effect, increasing the critical heat flux by more than 200%. Bubble behavior and heat transfer mechanisms on heating surfaces were further explored. The results show that a large electrical force can be generated at the junction of the conducting and insulating surfaces under the action of the electric field, which drives the bubbles in the cavity to departure quickly from the heating surface and avoids the formation of a vapor block. As the electric field intensity increases, the contact line produces pinning, which facilitates the formation of multiple continuously open vapor-liquid separation paths on the heating surface, resulting in a significant enhancement of the boiling heat transfer performance. Finally, a modified correlation equation is proposed to predict the critical heat flux under non-uniform electric field.

A bidirectional brain interface with both "write" and "read" functions can be an important tool for fundamental studies and potential clinical treatments for neurological diseases. Here we report a miniaturized multifunctional fiber based optoacoustic emitter (mFOE) that first integrates simultaneous non-genetic optoacoustic stimulation for "write" and electrophysiology recording of neural circuits for "read". The non-genetic feature addresses the challenges of the viral transfection required by optogenetics in primates and human. The orthogonality between optoacoustic waves and electrical field provides a solution to avoid the interference between electrical stimulation and recording. We first validated the non-genetic stimulation function of the mFOE in rat cultured neurons using calcium imaging. In vivo application of mFOE for successful simultaneous optoacoustic stimulation and electrical recording of brain activities was confirmed in mouse hippocampus in both acute and chronical applications up to 1 month. Minimal brain tissue damage has been confirmed after these applications. The capability of non-genetic neural stimulation and recording enabled by mFOE opens up new possibilities for the investigation of neural circuits and brings new insights into the study of ultrasound neurostimulation.

We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical expression of the efficiency at maximum power for this kind of engines. This expression satisfies the universal law of efficiency at maximum power up to the second order of the Carnot efficiency. We also analyze the issue of power at any given efficiency for general low-dissipation engines, and then obtain the supremum of the power in three limiting cases respectively., Comment: 10 pages, 7 figures

High precision neuromodulation is a powerful tool to decipher neurocircuits and treat neurological diseases. Current non-invasive neuromodulation methods offer limited precision at the millimeter level. Here, we report optically-generated focused ultrasound (OFUS) for non-invasive brain stimulation with ultrahigh precision. OFUS is generated by a soft optoacoustic pad (SOAP) fabricated through embedding candle soot nanoparticles in a curved polydimethylsiloxane film. SOAP generates a transcranial ultrasound focus at 15 MHz with an ultrahigh lateral resolution of 83 um, which is two orders of magnitude smaller than that of conventional transcranial-focused ultrasound (tFUS). Here, we show effective OFUS neurostimulation in vitro with a single ultrasound cycle. We demonstrate submillimeter transcranial stimulation of the mouse motor cortex in vivo. An acoustic energy of 0.6 mJ/cm^2, four orders of magnitude less than that of tFUS, is sufficient for successful OFUS neurostimulation. OFUS offers new capabilities for neuroscience studies and disease treatments by delivering a focus with ultrahigh precision non-invasively., Comment: 36 pages, 5 main figures, 13 supplementary figures

Neural interfaces using biocompatible scaffolds provide crucial properties for the functional repair of nerve injuries and neurodegenerative diseases, including cell adhesion, structural support, and mass transport. Neural stimulation has also been found to be effective in promoting neural regeneration. This work provides a new strategy to integrate photoacoustic (PA) neural stimulation into hydrogel scaffolds using a nanocomposite hydrogel approach. Specifically, polyethylene glycol (PEG)-functionalized carbon nanotubes (CNT), highly efficient photoacoustic agents, are embedded into silk fibroin to form biocompatible and soft photoacoustic materials. We show that these photoacoustic functional scaffolds enable non-genetic activation of neurons with a spatial precision defined by the area of light illumination, promoting neuron regeneration. These CNT/silk scaffolds offered reliable and repeatable photoacoustic neural stimulation. 94% of photoacoustic stimulated neurons exhibit a fluorescence change larger than 10% in calcium imaging in the light illuminated area. The on-demand photoacoustic stimulation increased neurite outgrowth by 1.74-fold in a dorsal root ganglion model, when compared to the unstimulated group. We also confirmed that photoacoustic neural stimulation promoted neurite outgrowth by impacting the brain-derived neurotrophic factor (BDNF) pathway. As a multifunctional neural scaffold, CNT/silk scaffolds demonstrated non-genetic PA neural stimulation functions and promoted neurite outgrowth, providing a new method for non-pharmacological neural regeneration.

In solids, charge polarity can one-to-one correspond to spin polarity phenomenologically, e.g. ferroelectricity/ferromagnetism, antiferroelectricity/antiferromagnetism, and even dipole-vortex/magnetic-vortex, but ferrielectricity/ferrimagnetism kept telling a disparate story in microscopic level. Since the definition of a charge dipole involves more than one ion, there may be multiple choices for a dipole unit, which makes most ferrielectric orders equivalent to ferroelectric ones, i.e. this ferrielectricity is not necessary to be a real independent branch of polarity. In this work, by using the spherical aberration-corrected scanning transmission electron microscope, we visualize a nontrivial ferrielectric structural evolution in BaFe2Se3, in which the development of two polar sub-lattices is out-of-sync, for which we term it as irreducible ferrielectricity. Such irreducible ferrielectricity leads to a non-monotonic behavior for the temperature-dependent polarization, and even a compensation point in the ordered state. Our finding unambiguously distinguishes ferrielectrics from ferroelectrics in solids., Comment: 15 figures

Creating magnetic semiconductors that work at warm circumstance is still a great challenge in the physical sciences. Here, we report the discovery of ferromagnetism in the metal-free perylene diimide semiconductor, whose Curie temperature is higher than 400 Kelvin. A solvothermal approach is used to reduce and dissolve the rigid-backbone perylene diimide crystallites, and radical anion aggregates were fabricated by the subsequent self-assembly and oxidation process. Magnetic measurements exhibit the ferromagnetic ordering with the saturated magnetization of 0.48 $\mu_{\rm B}$ per molecule and the appreciable magnetic anisotropy. X-ray magnetic circular dichroism spectra suggest the ferromagnetism stems from $\pi$ orbitals of radicals. Our findings unambitiously demonstrate the long-range ferromagnetic ordering can survive at room temperature in organic semiconductors, although which are intuitively regarded to be nonmagnetic., Comment: 22 pages, 11 figures, 1 table

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors)., Comment: Accepted by ISTTT 2017 (International Symposium on Transportation & Traffic Theory)

Magnetic impurities adsorbed on graphene are coupled magnetically via the itinerant electrons. This interaction opens a gap in the band structure of graphene. The result strongly depends on how the magnetic impurities are distributed. While random doping produces a semiconductor, if all or most impurities are located in the same sublattice, the spin degeneracy is removed and a spin-polarized semiconductor arises.